text: """
  Class representing a group of particles.
  """
  __all__ = ["ParticleTracker"]
  
  import astropy.units as u
  import numpy as np
  import scipy.interpolate as interp
  
  from astropy import constants
  
  from plasmapy.particles import atomic
  from plasmapy.utils.decorators import validate_quantities
  
  from . import particle_integrators
  
  
  class ParticleTracker:
      """
      Object representing a species of particles: ions, electrons, or simply
      a group of particles with a particular initial velocity distribution.
  
      Parameters
      ----------
      plasma : `Plasma`
          Plasma from which fields can be pulled.
  
      type : `str`
          Particle type. See `plasmapy.particles.ParticleLike` for suitable
          arguments. The default is a proton.
  
      n_particles : `int`
          Number of macroparticles. The default is a single particle.
  
      scaling : `float`
          Number of particles represented by each macroparticle.
          The default is 1, which means a :math:`1:1` correspondence between particles
          and macroparticles.
  
      dt : `astropy.units.Quantity`
          Duration of timestep
  
      nt : `int`
          Number of timesteps
  
      Attributes
      ----------
      x : `astropy.units.Quantity`
          Current position. Shape (n, 3).
  
      v : `astropy.units.Quantity`
          Current velocity. Shape (n, 3).
  
      position_history : `astropy.units.Quantity`
          History of position.  Shape (nt, n, 3).
  
      velocity_history : `astropy.units.Quantity`
          History of velocity. Shape (nt, n, 3).
  
      q : `astropy.units.Quantity`
          Charge of particle.
  
      m : `astropy.units.Quantity`
          Mass of particle.
  
      eff_q : `astropy.units.Quantity`
          Total charge of macroparticle.
  
      eff_m : `astropy.units.Quantity`
          Total mass of macroparticle.
  
      Examples
      ----------
      See `Particle Stepper Notebook`_.
  
      .. _`Particle Stepper Notebook`: ../notebooks/simulation/particle_stepper.ipynb
      """
  
      integrators = {"explicit_boris": particle_integrators.boris_push}
  
      _wip_integrators = {}
  
      _all_integrators = dict(**integrators, **_wip_integrators)
  
      @validate_quantities(dt=u.s)
      def __init__(
          self,
          plasma,
          particle_type="p",
          n_particles=1,
          scaling=1,
          dt=np.inf * u.s,
          nt=np.inf,
          integrator="explicit_boris",
      ):
  
          if np.isinf(dt) and np.isinf(nt):  # coverage: ignore
              raise ValueError("Both dt and nt are infinite.")
  
          self.q = atomic.integer_charge(particle_type) * constants.e.si
          self.m = atomic.particle_mass(particle_type)
          self.N = int(n_particles)
          self.scaling = scaling
          self.eff_q = self.q * scaling
          self.eff_m = self.m * scaling
  
          self.plasma = plasma
  
          self.dt = dt
          self.NT = int(nt)
          self.t = np.arange(nt) * dt
  
          self.x = np.zeros((n_particles, 3), dtype=float) * u.m
          self.v = np.zeros((n_particles, 3), dtype=float) * (u.m / u.s)
          self.name = particle_type
  
          self.position_history = np.zeros((self.NT, *self.x.shape), dtype=float) * u.m
          self.velocity_history = np.zeros((self.NT, *self.v.shape), dtype=float) * (
              u.m / u.s
          )
          # create intermediate array of dimension (nx,ny,nz,3) in order to allow
          # interpolation on non-equal spatial domain dimensions
          _B = np.moveaxis(self.plasma.magnetic_field.si.value, 0, -1)
          _E = np.moveaxis(self.plasma.electric_field.si.value, 0, -1)
  
          self.integrator = self._all_integrators[integrator]
  
          self._B_interpolator = interp.RegularGridInterpolator(
              (self.plasma.x.si.value, self.plasma.y.si.value, self.plasma.z.si.value),
              _B,
              method="linear",
              bounds_error=True,
          )
  
          self._E_interpolator = interp.RegularGridInterpolator(
              (self.plasma.x.si.value, self.plasma.y.si.value, self.plasma.z.si.value),
              _E,
              method="linear",
              bounds_error=True,
          )
  
      def _interpolate_fields(self):
          interpolated_b = self._B_interpolator(self.x.si.value) * u.T
          interpolated_e = self._E_interpolator(self.x.si.value) * u.V / u.m
          return interpolated_b, interpolated_e
  
      @property
      def kinetic_energy_history(self):
          r"""
          Calculate the kinetic energy history for each particle.
  
          Returns
          --------
          `~astropy.units.Quantity`
              Array of kinetic energies, shape (nt, n).
          """
          return (self.velocity_history ** 2).sum(axis=-1) * self.eff_m / 2
  
      def boris_push(self, init=False):
          r"""
          Implement the Boris algorithm for moving particles and updating their
          velocities.
  
          Arguments
          ----------
          init : `bool`, optional
              If `True`, does not change the particle positions and sets ``dt``
              to ``-dt/2``.
  
          Notes
          ----------
          The Boris algorithm is the standard energy conserving algorithm for
          particle movement in plasma physics. See [1]_ for more details.
  
          Conceptually, the algorithm has three phases:
  
          1. Add half the impulse from electric field.
          2. Rotate the particle velocity about the direction of the magnetic
             field.
          3. Add the second half of the impulse from the electric field.
  
          This ends up causing the magnetic field action to be properly
          "centered" in time, and the algorithm conserves energy.
  
          References
          ----------
          .. [1] C. K. Birdsall, A. B. Langdon, "Plasma Physics via Computer
                 Simulation", 2004, p. 58-63
          """
          b, e = self._interpolate_fields()
  
          if init:
              self.integrator(
                  self.x.copy(), self.v, b, e, self.q, self.m, -0.5 * self.dt,
              )  # we don't want to change position here
          else:
              self.integrator(
                  self.x, self.v, b, e, self.q, self.m, self.dt,
              )
  
      def run(self):
          r"""
          Run a simulation instance.
          """
          self.boris_push(init=True)
          self.position_history[0] = self.x
          self.velocity_history[0] = self.v
          for i in range(1, self.NT):
              self.boris_push()
              self.position_history[i] = self.x
              self.velocity_history[i] = self.v
  
      def __repr__(self, *args, **kwargs):
          return (
              f"Species(q={self.q:.4e},m={self.m:.4e},N={self.N},"
              f'name="{self.name}",NT={self.NT})'
          )
  
      def __str__(self):  # coverage: ignore
          return (
              f"{self.N} {self.scaling:.2e}-{self.name} with "
              f"q = {self.q:.2e}, m = {self.m:.2e}, "
              f"{self.saved_iterations} saved history "
              f"steps over {self.NT} iterations"
          )
  
      def plot_trajectories(self):  # coverage: ignore
          r"""Draw trajectory history."""
          import matplotlib.pyplot as plt
  
          from astropy.visualization import quantity_support
          from mpl_toolkits.mplot3d import Axes3D
  
          quantity_support()
          fig = plt.figure()
          ax = fig.add_subplot(111, projection="3d")
          for p_index in range(self.N):
              r = self.position_history[:, p_index]
              x, y, z = r.T
              ax.plot(x, y, z)
          ax.set_title(self.name)
          ax.set_xlabel("$x$ position")
          ax.set_ylabel("$y$ position")
          ax.set_zlabel("$z$ position")
          plt.show()
  
      def plot_time_trajectories(self, plot="xyz"):  # coverage: ignore
          r"""
          Draw position history versus time.
  
          Parameters
          ----------
          plot : `str`, optional
              Enable plotting of position component x, y, z for each of these
              letters included in `plot`.
          """
          import matplotlib.pyplot as plt
  
          from astropy.visualization import quantity_support
          from mpl_toolkits.mplot3d import Axes3D
  
          quantity_support()
          fig, ax = plt.subplots()
          for p_index in range(self.N):
              r = self.position_history[:, p_index]
              x, y, z = r.T
              if "x" in plot:
                  ax.plot(self.t, x, label=f"x_{p_index}")
              if "y" in plot:
                  ax.plot(self.t, y, label=f"y_{p_index}")
              if "z" in plot:
                  ax.plot(self.t, z, label=f"z_{p_index}")
          ax.set_title(self.name)
          ax.legend(loc="best")
          ax.grid()
          plt.show()
  
      def test_kinetic_energy(self):
          r"""Test conservation of kinetic energy."""
          assert np.allclose(
              self.kinetic_energy_history,
              self.kinetic_energy_history.mean(),
              atol=3 * self.kinetic_energy_history.std(),
          ), "Kinetic energy is not conserved!"
  